The Republican candidates say that proliferating private health insurance plans will lead to innovation and cost-cutting. So far, the evidence isn’t there.

Mitt Romney and Paul Ryan say that their Medicare plan will lower costs by making the program more competitive. The argument goes like this: Private health insurance plans and traditional Medicare all submit bids to the government every year showing the price at which they would insure beneficiaries. The government gives seniors an allowance—“premium support”—based on those competing plans. (Seniors who choose low-cost plans could keep the savings; those who choose pricey ones would need to reach into their pockets.) Insurers would force providers to lower the cost of care; they, in turn, could lower their prices to compete with each other; and the cheaper plans would drive the growth of Medicare spending down. “Look,” Romney said on NBC’s Meet the Press last Sunday, “competition works.”

That sounds logical, but it’s so untested that even the experts who are the most enthusiastic about the approach say they don’t know to what degree competition will slow spending. No one this cycle—not the Congressional Budget Office, not the Heritage Foundation, not even the Romney campaign—has estimated the effect. Romney’s voucher plan could generate savings (and not necessarily by shifting costs to seniors), but even proponents admit that it would amount to a huge gamble on a yet-unmeasured mechanism for slowing growth. The most sympathetic view possible of competition is that it might not work.

Evidence exists that private plans could offer cheaper coverage than traditional Medicare in some markets—and that, given a choice of comparable plans, many Americans would pick low price tags. Academic boosters of premium support say that it shows a path for lowering costs right away. Roger Feldman, a professor at the University of Minnesota who has written extensively about the virtues of premium support, estimated in a recent paper for the conservative American Enterprise Institute that simply taking advantage of lower bids could save the Medicare program more than $339 million over 10 years, with most of the savings in a few large markets where studies suggest that the government overpays.

But when it comes to restraining the rate of growth in Medicare spending, which typically exceeds overall economic growth, Feldman makes no promises. “I don’t build that in,” he says, “because I don’t think the evidence is strong enough.” Conservative think tanks have tried to model the savings that might come from similar voucher-based reforms. They, too, have shied away from calculating the degree to which competition might stem growth. The Heritage Foundation has published a reform plan that it says could reduce Medicare’s spending by $702 billion over 10 years, but it estimates no savings from competition’s effect on the health sector. “It’s kind of like trying to find the Higgs particle in health care,” says Rea Hederman Jr., a research fellow at Heritage who worked on the study. “We know it’s out there, but we don’t have the tools to find it.”

The trouble is that there are basically no examples of this in the U.S. health care system, in part because our health insurance market doesn't function this way. Most Americans get insurance from their employer rather than choosing a policy themselves. And most Medicare beneficiaries still get their benefits from the government program, which has historically grown more slowly than health spending overall.

Competition could, in fact, cause the opposite of the intended effect. When lots of insurers split the market, they can undercut their ability to demand new, cost-saving payment and treatment methods from providers. Instead, small insurers often end up paying the prices that big hospital groups dictate. Several analyses conclude that, in parts of the country with powerful hospitals, Medicare will continue to be the lowest bidder, even if premium support works. Hederman estimates that half of Americans live in such areas. Critics also point out that, historically, insurers have made more money by catering to healthy patients, not by lowering the cost of care. And sophisticated industry strategies could rig a system to keep the sickest seniors out of private plans while reaping overpayments for the healthy.

Advocates of premium support say that despite the limited evidence, it’s worth trying. They point to the instant savings that would come when beneficiaries select lower private bids in expensive markets. And they say that given Medicare’s long-term budget problems, any valid cost-saving theory should be tested. But even premium support’s biggest boosters concede it’s unlikely that Ryan’s plan could meet the kind of annual growth cap that he envisions.